Highschool Test Scores
Matthew Hondrakis
14 November 2021
Student Test Scores
Structure of Data Set
str(stest)## spec_tbl_df[,8] [1,000 x 8] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ gender : Factor w/ 2 levels "A","B": 1 1 1 2 2 1 1 2 2 1 ...
## $ race/ethnicity: Factor w/ 5 levels "group A","group B",..: 2 3 2 1 3 2 2 2 4 2 ...
## $ parent ed : Factor w/ 6 levels "some high school",..: 5 3 6 4 3 4 3 3 2 2 ...
## $ lunch : Factor w/ 2 levels "standard","free/reduced": 1 1 1 2 1 1 1 2 2 2 ...
## $ test prep : Factor w/ 2 levels "none","completed": 1 2 1 1 1 1 2 1 2 1 ...
## $ math : num [1:1000] 72 69 90 47 76 71 88 40 64 38 ...
## $ reading : num [1:1000] 72 90 95 57 78 83 95 43 64 60 ...
## $ writing : num [1:1000] 74 88 93 44 75 78 92 39 67 50 ...
## - attr(*, "spec")=
## .. cols(
## .. gender = col_factor(levels = NULL, ordered = FALSE, include_na = FALSE),
## .. `race/ethnicity` = col_factor(levels = NULL, ordered = FALSE, include_na = FALSE),
## .. `parental level of education` = col_factor(levels = NULL, ordered = FALSE, include_na = FALSE),
## .. lunch = col_factor(levels = NULL, ordered = FALSE, include_na = FALSE),
## .. `test preparation course` = col_factor(levels = NULL, ordered = FALSE, include_na = FALSE),
## .. `math score` = col_double(),
## .. `reading score` = col_double(),
## .. `writing score` = col_double()
## .. )Correlation Plot
stest %>%
select(math, writing, reading) %>%
ggpairs()
There is a clear correlation between the pair of scores. With the highest correlation coefficient of 0.9545981 being between Reading and Writing.
By Gender
Math
ggplot(stest, aes(`math`, color = `gender`)) +
geom_density() + theme_classic()
ggplot(stest, aes(y = `math`, color = `gender`)) +
geom_boxplot() + theme_classic() + theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank())
The variance is approximately the same and they are normally distributed. Thus, We can conduct a t-test to evaluate whether the difference in means between the two groups is statistically significant.
t.test(stest$`math`~stest$gender, conf.level = 0.99)##
## Welch Two Sample t-test
##
## data: stest$math by stest$gender
## t = -5.398, df = 997.98, p-value = 8.421e-08
## alternative hypothesis: true difference in means is not equal to 0
## 99 percent confidence interval:
## -7.530918 -2.659105
## sample estimates:
## mean in group A mean in group B
## 63.63320 68.72822With 99% confidence, we can assume the difference in means between the two genders is between (-7.52,-2.66).
Writing
ggplot(stest, aes(`writing`, color = `gender`)) +
geom_density() + theme_classic()
ggplot(stest, aes(y = `writing`, color = `gender`)) +
geom_boxplot() + theme_classic() + theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank())
It appears that in the case of writing, it is gender A that scores better than gender B.
t.test(stest$`writing`~stest$gender, conf.level = 0.99)##
## Welch Two Sample t-test
##
## data: stest$writing by stest$gender
## t = 9.9977, df = 997.53, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 99 percent confidence interval:
## 6.792495 11.519462
## sample estimates:
## mean in group A mean in group B
## 72.46718 63.31120As we expected, with 99% confidence, we can assume the difference in means between the two genders is between (6.79,11.52). The disparity in scores is much greater for writing than it is for math.
By Race
Math
ggplot(stest, aes(`math`, color = `race/ethnicity`)) +
geom_density() + theme_classic()
ggplot(stest, aes(y = `math`, color = `race/ethnicity`)) +
geom_boxplot() + theme_classic() + theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank())
An Analysis of Variance would provide more insight into the possible group differences.
summary(aov(math~`race/ethnicity`, stest))## Df Sum Sq Mean Sq F value Pr(>F)
## `race/ethnicity` 4 12729 3182 14.59 1.37e-11 ***
## Residuals 995 216960 218
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Sorted by Food
stest %>%
ggplot(aes(y = math, color = `race/ethnicity`)) + geom_boxplot() +
theme_bw() + theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank()) +
facet_wrap(~ lunch)
Sorted by Test Prep
stest %>%
ggplot(aes(y = math, color = `race/ethnicity`)) + geom_boxplot() +
theme_bw() + theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank()) +
facet_wrap(~ `test prep`)
Writing
ggplot(stest, aes(`writing`, color = `race/ethnicity`)) +
geom_density() + theme_classic()
ggplot(stest, aes(y = `writing`, color = `race/ethnicity`)) +
geom_boxplot() + theme_classic() + theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank())
The difference is less clear with respect to writing. Running an ANOVA test here may provide more answers.
summary(aov(writing~`race/ethnicity`, stest))## Df Sum Sq Mean Sq F value Pr(>F)
## `race/ethnicity` 4 6456 1614.0 7.162 1.1e-05 ***
## Residuals 995 224221 225.3
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1By Parent’s Education
Math
ggplot(stest, aes(`math`, color = `parent ed`)) +
geom_density() + theme_classic()
ggplot(stest, aes(y = `math`, color = `parent ed`)) +
geom_boxplot() + theme_classic() + theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank())
Writing
ggplot(stest, aes(`writing`, color = `parent ed`)) +
geom_density() + theme_classic()
ggplot(stest, aes(y = `writing`, color = `parent ed`)) +
geom_boxplot() + theme_classic() + theme(axis.text.x = element_blank(),
axis.ticks.x = element_blank())
Scrap
Test prep by Parent education
counted <- stest %>%
group_by(`parent ed`) %>%
count(`test prep`) %>%
mutate(n = n/sum(n)) %>%
arrange(desc(n))
ggplot(counted, aes(n, fct_inorder(`parent ed`), fill = `test prep`)) +
theme_bw() + geom_col() + ylab("Percent")
stest %>%
group_by(`parent ed`) %>%
count(lunch) %>%
mutate(n = n/sum(n)) %>%
ggplot(aes(n, `parent ed`, fill = lunch)) + geom_col() + theme_bw() +
ylab("Percent")
stest %>%
filter(`race/ethnicity` == "group A") %>%
ggplot(aes(math, color = `test prep`)) + geom_density() +
theme_bw()
p <- stest %>%
ggplot(aes(math, color = `test prep`)) + geom_density() +
theme_bw() + facet_wrap(~ `race/ethnicity`)
ggplotly(p)